This paper presents a refined higher-order shear deformation theory for the linear and geometrically non-linear finite element analysis of fibre reinforced composite and sandwich laminates Laminae material is assumed to be linearly elastic, homogeneous and isotropic/orthotropic. This theory accounts for parabolic distribution of the transverse shear strains through the thickness of the laminate and higher-order terms in Green's strain vector in the sense of von Karman. A simple C0 finite element formulation is presented with a total Lagrangian approach and a nine-node Lagrangian quadrilateral element is chosen with nine degrees of freedom per node. Numerical results are presented for linear and geometric non-linear analysis of multi-layer cross-ply laminates and sandwich plates. The present theory predicts displacements and stresses more accurately than the first-order shear deformation theory. The results are compared with available closed-form and numerical solutions of both three-dimensional elasticity and plate theories.